I will review recent progress in designing and perturbing flatband networks - tight binding lattices which host macroscopically degenerate flat spectral bands. Their origin is rooted in local symmetries of the lattice, with destructive interference leading to the existence of compact localized eigenstates, which have been recently experimentally detected in photonic and semiconductor devices. Weak disorder hybridizes compact eigenstates with dispersive bands, leading to Fano resonances, Cauchy-tailed effective disorder potentials, and singular mobility edges, among others. I will discuss recent results on designing flatbands using a systematic flatband generator approach based on local lattice properties, and review further progress in the field.